Preheat your air fryer to 375°F (190°C) for 3-5 minutes.
In a medium sized mixing bowl, add the drained tuna, mayonnaise, diced red onion, diced celery, chopped fresh parsley, lemon juice, Dijon mustard, salt, and black pepper and mix well.
Butter the outer sides of each slice of bread evenly.
On one side of the bread, spread a generous portion of the tuna salad mixture. One the other slice of bread, place two slices of cheddar cheese. Place the top onto the bottom.
Carefully place the prepared tuna melt sandwiches into the air fryer basket, ensuring they are not overlapping.
Air fry the tuna melts at 375°F (190°C) for 5-7 minutes, flipping halfway. The bread should be golden brown and crispy, and the cheese is melted and bubbly.
Once cooked, carefully remove the tuna melts from the air fryer and let them cool for a minute before serving.